The Indian Ocean dipole (IOD) is one of the main modes characterizing the interannual variability of the large-scale ocean–atmosphere interaction in the equatorial zone of the World Ocean. A dipole manifests itself as an out-of-phase interannual fluctuation of the ocean–atmosphere characteristics in the western and eastern parts of the equatorial–tropical zone of the Indian Ocean. IOD can be a consequence of the ENSO (El Niño–Southern Oscillation) events in the Pacific Ocean, or it can be independent of them and arise due to the Indian Ocean inherent processes. Earlier, it was suggested that the generation of the long planetary waves in the Indian Ocean by the ENSO events is one of the mechanisms of the ENSO impact on the IOD. However, quite often, such a mechanism is not the case and IOD is generated itself as an independent Indian Ocean mode. We hypothesized that this generation is due to the growing oceanic disturbances, as a result of instability of the system of Indian Ocean zonal currents in the vicinity of the critical layer, in which the phase velocity of Rossby waves is equal to the average velocity of the zonal currents. In the present work, the study of the features of the formation of the critical layer in the equatorial–tropical zone of the Indian Ocean is continued using different oceanic re-analyses and standard theory of the Rossby waves. As a result of comparison of different re-analyses data with the RAMA (The Research Moored Array for African-Asian-Australian Monsoon Analysis and Prediction) measurements, the operative re-analysis ORAS5 output of European Centre for Medium-Range Weather Forecasts (ECMWF) on potential temperature, salinity, and the zonal component of the currents’ velocity for the period 1979–2018 was used. Monthly profiles of potential temperature, salinity, and the zonal component of the currents’ velocity were selected from the ORAS5 archive for the sections situated between 7.5–15.5° S and 50–100° E. From these data and for each month, using the standard theory of planetary waves, the phase velocity of the lowest baroclinic mode of the Rossby long waves was calculated and the critical layers were determined. For each critical layer, its length was calculated. The obtained time series of the length of the critical layers were compared to the variability of dipole mode index (DMI). It is shown that the majority of the cases of the IOD generation as inherent (independent on the Pacific processes) mode were accompanied by the critical layer formation in the region of interest. Usually, the critical layers occur in spring, one to two months before the onset of the positive IOD events. This indicates that the presence of instability in the system of the zonal currents can be a reason for the generation of IOD and the asymmetry of the amplitude of the dipole mode index between positive and negative events. During the extremely intense ENSO event of 1997–1998, which was accompanied by the strong IOD event, the critical layer in the equatorial–tropical zone of the Indian Ocean was absent. This ENSO event generated the oceanic planetary waves at the eastern edge of the Indian Ocean. Therefore, it is shown that the above mechanism of the ENSO–IOD interaction is a reality.